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1.
In this paper, we consider the Sturm–Picone comparison theorem of conformable fractional differential equations on arbitrary time scales. Since the Picone identity plays an important role in discussing the Sturm comparison theorem. Firstly, we establish the Picone identity of conformable fractional differential equations on arbitrary time scales. By using this identity, we obtain our main result—the Sturm–Picone comparison theorem of conformable fractional differential equations on time scales. This result not only extends and improves the corresponding continuous and discrete time statement, but also contains the usual time scale case when the order of differentiation is one.  相似文献   

2.
In this paper, we establish a nonlinear analogue of Picone’s identity for biharmonic operators on Heisenberg group. As an applications of Picone’s identity, we obtain Hardy-Rellich type inequality, Morse index, Caccioppoli inequality, Picone inequality for biharmonic operators on Heisenberg group.  相似文献   

3.
本文给出了齐次群上的一类广义Picone型恒等式,由此证明了以下半线性方程组(其中 表示齐次群上的广义梯度)的Sturmian比较定理及一类振荡定理,并用于Heisenberg群上一类半线性方程.然后利用这里的广义Picone型恒等式证明了Heisenberg群上一类更一般的Hardv型不等式  相似文献   

4.
The purpose of this note is to show a generalization to Picone’s identity in a nonlinear framework. The classical Picone’s identity turns out to be a particular case of our result. We show, as an application of our results, that the Morse index of the zero solution to a semilinear elliptic boundary value problem is 0 and also establish a linear relationship between the components of the solution of a nonlinear elliptic system.  相似文献   

5.
二阶非线性微分方程的Picone恒等式与Sturm比较定理   总被引:2,自引:0,他引:2       下载免费PDF全文
该文推广了Picone恒等式,由此得到了二阶非线性方程解的零点比较定理。  相似文献   

6.
Ukrainian Mathematical Journal - We prove a nonlinear analog of Picone’s identity for the ?γ -Laplace operator. As an application, we give a Hardy-type inequality and the Sturmian...  相似文献   

7.
Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.  相似文献   

8.
关于一类向量场的Picone恒等式和Hardy不等式1   总被引:10,自引:0,他引:10  
张慧清  钮鹏程 《数学杂志》2003,23(1):121-125
本文给出了构成Baouendi-Grushin算子 的向量场的Picone恒 式,由此导出了Hardy不等式.已有文献中得到的不等式成为本文结果的特殊情形。  相似文献   

9.
In this paper we present a Hardy type inequality and a Picone type identity for the real sub-Laplacian on the homogeneous group. The existence of the indefinite eigenvalue problem and the simplicity of the principal eigenvalue are proved.  相似文献   

10.
In this paper a variety of nonexistence results are obtained for positive solutions to the m-Laplacean and related equations by means of generalized Picone Identity arguments. These procedures allow the treatment of nonradial problems and extend several recent theorems.  相似文献   

11.
王永忠  崔学伟 《应用数学》2011,24(2):279-283
本文在有界正则域内研究了一类加权拟线性抛物方程组.由单个抛物方程相关的已知结论得到此类方程组的非负entropy解的正下界,然后利用一般的Picone恒等式并构造适当的检验函数,证明此类方程组的非负entropy解不存在.  相似文献   

12.
Summary Nonoscillation theorems for perturbed second order nonlinear differential equations are obtained. A nonlinear Picone type identity is introduced to obtain some Sturm-Picone type comparison theorems for nonlinear equations. Entrata in Redazione il 19 gennaio 1977. Research supported by the Mississippi State University Biological and Physical Sciences Research Institute.  相似文献   

13.
We prove the global existence, uniqueness, and positivity of solutions to the Cauchy problem, with general initial data, for a class of generalized Boltzmann models with dissipative collisions.  相似文献   

14.
对构成广义Greiner算子的向量场$X_j = \frac{\partial }{\partial x_j} + 2ky_j \vert z\vert ^{2k - 2}\frac{\partial }{\partialt}$, $Y_j = \frac{\partial }{\partial y_j } - 2kx_j \vert z\vert^{2k - 2}\frac{\partial }{\partial t}$, j = 1,... ,n, x,y∈ Rn, $z = x + \sqrt { - 1} \,y$, t ∈ R, k ≥1, 得到了拟球域内和拟球域外的Hardy型不等式;建立了广义Picone型恒等式,并由此导出比文献[3]更一般的全空间上的Hardy型不等式;并在$p = 2$时建立了具最佳常数的Hardy型不等式.  相似文献   

15.
The study of a particular two-dimensional system of second-order ordinary differential equations with nonlinear monotone coefficients led to the results in this paper. Systematic use of the Picone identity is made. The techniques when applied to scalar equations generalize a comparison result of Bobisud and Grimmer and Waltman, and further, can be applied to certain functional differential equations. The natural extension to higher dimensions is given. Finally, a comparison theorem for the original system is given along with its relationship to a corresponding boundary value problem.  相似文献   

16.
The well known mean value property for polyharmonic functions in the ball (see Picone [9], Bramble-Payne [2]) is generalized to the case of an annular domain. We prove that the Peano kernel arising from this new mean value property has definite sign. It is a polyspline in the sense of [8]. The present results generalize former investigations concerning the Peano kernel associated with the mean value property of polyharmonic functions in the ball.  相似文献   

17.
Picone type formula for half‐linear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Employing the formula, Leighton and Sturm–Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

18.
We employ a version of the Picone Identity, suitable for the -Laplacean, to obtain a Sturm Comparison Theorem for generalized solutions. This answers a question posed by Dunninger in 1995.

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19.
A necessary and sufficient condition for the identity matrix to be the unique Lyapunov scaling factor of a given real symmetric matrix A is given. This uniqueness is shown to be equivalent to the uniqueness of the identity matrix as a scaling D for which the kernels of A and AD are identical.  相似文献   

20.
本文考虑一类具有脉冲扰动的比率相关的捕食者一食饵扩散模型,利用比较原理研究了这类系统的持续生存和灭绝性,通过将脉冲反应扩散方程转化为相应的算子方程,并证明了解在适当空间的紧性,得到了周期解的存在性、唯一性和全局稳定性.最后分析了脉冲效应对系统性态的影响.  相似文献   

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